A075126 Number of bargraphs of site-perimeter n.
0, 0, 0, 1, 0, 2, 2, 4, 8, 14, 26, 52, 97, 193, 377, 752, 1500, 3022, 6107, 12429, 25365, 52042, 107090, 221235, 458316, 952439, 1984262, 4144601, 8676232, 18202536, 38263456, 80585694, 170013976, 359277183, 760400787, 1611721413, 3420839200, 7270098883
Offset: 1
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..1000
- M. Bousquet-Mélou and A. Rechnitzer, The site-perimeter of bargraphs, Adv. in Appl. Math. 31 (2003), 86-112.
Programs
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Maple
b:= proc(n, y, t, w) option remember; `if`(n<0, 0, `if`(n=0, (1-t), `if`(t<0, 0, b(n-`if`(w>0 or t=0, 1, 2), y+1, 1, max(0, w-1)))+ `if`(t>0 or y<2, 0, b(n, y-1, -1, `if`(t=0, 1, w+1)))+ `if`(y<1, 0, b(n-`if`(t<0, 1, 2), y, 0, `if`(t<0, w, 0))))) end: a:= n-> b(n, 0, 1, 0): seq(a(n), n=1..45); # Alois P. Heinz, Jun 05 2016 -
Mathematica
b[n_, y_, t_, w_] := b[n, y, t, w] = If[n<0, 0, If[n==0, 1-t, If[t<0, 0, b[n - If[w>0 || t==0, 1, 2], y+1, 1, Max[0, w-1]]] + If[t>0 || y<2, 0, b[n, y-1, -1, If[t==0, 1, w+1]]] + If[y<1, 0, b[n - If[t<0, 1, 2], y, 0, If[t<0, w, 0]]]]]; a[n_] := b[n, 0, 1, 0]; Table[a[n], {n, 1, 45}] (* Jean-François Alcover, Nov 28 2016 after Alois P. Heinz *)
Formula
The generating function is known in closed form. Closed, but complicated. It is proved to be non-D-finite.
Extensions
Offset corrected by Alois P. Heinz, Jun 04 2016
a(31)-a(38) from Alois P. Heinz, Jun 05 2016
Comments